In an industrial measuring system or a medical imaging system, such as an X-ray Computerized Scanner or a Magnetic Resonance Imaging (MRI) Scanner, it is necessary to distinguish three-dimensional objects from each other or to separate the three-dimensional objects so they can be accurately counted. It is well-known to separate two-dimensional connected components by a "labeling process" used in a conventional two-dimensional image processor. In the labeling process, each pixel must be two-dimensionally checked to determine if it is connected to adjacent pixels, all belonging to the same connected component. If the pixel is determined to be connected to an already identified component, it is labeled with the same component number given to that component. If the pixel is determined not to be connected to an already identified component, it is given or labeled with a new component number. After all pixels in an image are checked, a new image whose connected components are labeled is obtained. Such a labeling process is described, for example, in Chapter 9.1.3 entitled Component Labeling and Counting in the book by Azriel Rosenfeld and Avimash C. Kak, "Digital Picture Processing."
For separating and distinguishing three-dimensional objects in a three-dimensional image, a three-dimensional labeling technique was developed as described in T. Yonekura et al. in "Connectivity and Euler Number of Figures in the Digitized Three-Dimensional Space", Japanese Electronics and Communication Association Papers (D), J65-D, 1, pp. 1-24 (1981). However, the technique is merely an extension of the two-dimensional labeling technique applied to a three-dimensional image. Each pixel is also three-dimensionally checked to determine if it is connected to pixels identified with other connected components. Thus, it requires a large number of calculations and much time to accomplish three-dimensional labeling using this method.